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In the first problem, it looks like the student is calculating the moment arm as if the pivot is at the 40cm mark. In the second, it seems that the student has assumed that the moment arm is 40cm, and in the 3rd the student seems to have made an error with the proper trig function (cosine instead of sine) and has made their moment arm the horizontal distance from the pivot to the tip.

Each student seems to understand the idea that you need the perpendicular component of the force to find the torque, but they all seem deeply confused about how to find the moment arm in this situation.

I’d probably ask the student to explain to me what the is that they are calculating in the equation .

In the first one, the student is determining the size of the moment arm by the size of the vector as drawn. They don’t understand that the size of the arrow doesn’t matter; the only important thing shown graphically is its base. I’m a bit stumped on how to get the student to realize this – maybe ask what units the force has, and what units the ruler has?

In the second, the student assumes the moment arm is at 0. This might be a “silly mistake” made in haste, but the student should be familiar with the idea that not all measurements start from zero. If he or she had been exposed to kinematics problems where objects start in motion, or not at distance and time 0, perhaps that could have been extended to this problem.

John, I’m fairly sure the third one uses the correct trig function, because the angle used is 60˚. It would have been clearer to draw the triangle on the other side of the vector, but students rarely realize the two are equivalent. My guess is that it has something to do with imagining the triangle “falling” to the bottom of the page and not wanting to have it “cantilevered” out. Alternatively, she could have labelled the other acute interior angle 60˚, and indeed the perpendicular side is the adjacent side to that, hence cosine. It’s not a sine error, it’s a sign error, since the problem says clockwise is positive. I feel that this is something of a “gotcha” because that’s opposite of how the right hand rule works: +k is counterclockwise.